Linear sigma models with torsion

Abstract

Gauged linear sigma models with (0, 2) supersymmetry allow a larger choice of couplings than models with (2, 2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models with branes. As a non-compact example, we describe a family of metrics which correspond to deformations of the heterotic conifold by turning on H-flux. We then describe compact models which are gauge-invariant only at the quantum level. Our construction gives a generalization of symplectic reduction. The resulting spaces are non-Kähler analogues of familiar toric spaces like complex projective space. Perturbatively conformal models can be constructed by considering intersections.